Parameter Optimization for Excitable Cell Models

The electrophysiology of nodose ganglia neurons is of great interest in the analysis of cell membrane currents and action potential behavior. This behavior was initially outlined in the Hodgkin-Huxley conductance model [1] using a system of nonlinear differential equations. Later, Schild et al. [2] developed an extension of the Hodgkin-Huxley model to provide a more exhaustive description of ion channels involved in nodose neuronal action potential activity. We consider a variety of methods to fit the parameters of both the Hodgkin-Huxley and Schild et al. models to an empirical stimulus response dataset. Our methods were validated using synthetic datasets, as well as voltage-clamp data for nodose neurons. The fitting procedure that we implemented demonstrates the predictive efficacy of the Schild et al. model as well as its ability to provide a superior characterization of electrical signatures of nodose neurons

Macroscopic equations governing noisy spiking neuronal populations

At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely relied on heuristic partial (and partially justified) macroscopic models, which successfully reproduced a number of relevant phenomena. The relationship between these macroscopic models and the spiking noisy dynamics of the underlying cells has since then been a great endeavor. Based on recent mean-field reductions for such spiking neurons, we present here {a principled reduction of large biologically plausible neuronal networks to firing-rate models, providing a rigorous} relationship between the macroscopic activity of populations of spiking neurons and popular macroscopic models, under a few assumptions (mainly linearity of the synapses). {The reduced model we derive consists of simple, low-dimensional ordinary differential equations with} parameters and {nonlinearities derived from} the underlying properties of the cells, and in particular the noise level. {These simple reduced models are shown to reproduce accurately the dynamics of large networks in numerical simulations}. Appropriate parameters and functions are made available {online} for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley models

Differential Behavioral Responses to\ud Cocaethylene of Long-Evans and\ud Sprague-Dawley Rats: Role of Serotonin

Cocaethylene is a neuroactive metabolite derived from the concurrent consumption of cocaine and ethanol. The effects of cocaethylene on locomotor activity, stereotypy, and rearing in Long-Evans and Sprague-Dawley rats were compared.A single cocaine injection (molar equivalent of 60 μmol/kg cocaethylene, intraperitoneal) elicited a robust series of motor output behaviors, including locomotion, stereotypy, and rearing over a 30-minute testing period in Long-Evans rats. In contrast, cocaethylene administration,\ud under comparable testing conditions, produced no significant changes in locomotor and investigatory behaviors. Because cocaethylene has relatively little impact on serotonin (5-HT) reuptake as opposed to reuptake of dopamine, we pretreated Long-Evans rats with fluoxetine (10 mg/kg; IP), a selective 5-HT reuptake inhibitor. Fluoxetine profoundly augmented cocaethylene-stimulated behaviors in this rat phenotype. To examine whether other rat strains exhibit a similar response to cocaethylene, Sprague-Dawley rats were injected (IP) with cocaethylene and their behavior patterns monitored over a 30-minute testing period. Cocaethylene produced marked locomotor and exploratory behaviors in this strain, suggesting therefore that Long-Evans and Sprague-\ud Dawley rats differ in their response to cocaethylene. To relate these behavioral differences to possible structural differences in the neuronal density of dopaminergic or\ud serotonergic neurons, Long-Evans and Sprague-Dawley brains were evaluated for tyrosine hydroxylase and 5-HT immunocytochemistry. No gross morphological differences\ud in neuronal architecture or density were found in the ventral tegmental area or dorsal raphe nucleus of the two rat phenotypes. These results indicate that two commonly used rat strains show a differential response to cocaethylene and the neurochemical basis for this behavioral difference may be related to synaptic 5-HT bioavailability

Die Rolle der Zielnähe und der investierten Anstrengung für den erwarteten Wert einer Handlung

In human neuroscientific research, there has been an increasing interest in how the brain computes the value of an anticipated outcome. However, evidence is still missing about which valuation related brain regions are modulated by the proximity to an expected goal and the previously invested effort to reach a goal. The aim of this dissertation is to investigate the effects of goal proximity and invested effort on valuation related regions in the human brain. We addressed this question in two fMRI studies by integrating a commonly used reward anticipation task in differential versions of a Multitrial Reward Schedule Paradigm. In both experiments, subjects had to perform consecutive reward anticipation tasks under two different reward contingencies: in the delayed condition, participants received a monetary reward only after successful completion of multiple consecutive trials. In the immediate condition, money was earned after every successful trial. In the first study, we could demonstrate that the rostral cingulate zone of the posterior medial frontal cortex signals action value contingent to goal proximity, thereby replicating neurophysiological findings about goal proximity signals in a homologous region in non-human primates. The findings of the second study imply that brain regions associated with general cognitive control processes are modulated by previous effort investment. Furthermore, we found the posterior lateral prefrontal cortex and the orbitofrontal cortex to be involved in coding for the effort-based context of a situation. In sum, these results extend the role of the human rostral cingulate zone in outcome evaluation to the continuous updating of action values over a course of action steps based on the proximity to the expected reward. Furthermore, we tentatively suggest that previous effort investment invokes processes under the control of the executive system, and that posterior lateral prefrontal cortex and the orbitofrontal cortex are involved in an effort-based context representation that can be used for outcome evaluation that is dependent on the characteristics of the current situation.Derzeit besteht im Bereich der Neurowissenschaften ein großes Interesse daran aufzuklären, auf welche Weise verschiedene Variablen die Wertigkeit eines erwarteten Handlungsziels beeinflussen bzw. welche Hirnregionen an der Repräsentation der Wertigkeit eines Handlungsziels beteiligt sind. Die meisten Untersuchungen beziehen sich dabei auf Einflussgrößen wie die erwartete Belohnungshöhe, die Wahrscheinlichkeit, mit der ein bestimmtes Ereignis eintritt, oder die Dauer bis zum Erhalt einer Belohnung. Bisher liegen jedoch kaum Untersuchungen vor bezüglich zweier anderer Variablen, die ebenfalls den erwarteten Wert eines Handlungsergebnisses beeinflussen. Das sind (a) die Nähe zu dem erwarteten Ziel und (b) die bisher investierte Anstrengung, um ein Ziel zu erreichen. Das Ziel der vorliegenden Dissertation ist zu untersuchen, wie die Nähe zum Ziel und die bisher investierte Anstrengung Gehirnregionen beeinflussen, die mit der Repräsentation von Wertigkeit im Zusammenhang stehen. Dazu führten wir zwei fMRT-Studien durch, in denen wir eine klassische Belohnungs-Antizipationsaufgabe in unterschiedliche Versionen eines „Multitrial Reward Schedule“ Paradigmas integriert haben. Das bedeutet, dass die Probanden Belohnungs-Antizipationsaufgaben unter zwei unterschiedlichen Belohnungskontingenzen bearbeiteten: In der verzögerten Bedingung erhielten die Probanden einen Geldbetrag nach der erfolgreichen Bearbeitung von mehreren aufeinanderfolgenden Aufgaben, in der direkten Bedingung dagegen nach jeder korrekt ausgeführten Aufgabe. In der ersten Studie konnte eine sukzessiv ansteigende Aktivität in Abhängigkeit zur Zielnähe in der rostralen cingulären Zone identifiziert werden. Das deutet darauf hin, dass dieses Areal den Wert einer Handlung in Abhängigkeit zur Nähe zum Ziel kodiert. Die Ergebnisse der zweiten Studie zeigten, dass die bisher investierte Anstrengung kortikale Regionen moduliert, die klassischerweise mit kognitiven Kontrollfunktionen in Zusammenhang gebracht werden. Außerdem repräsentierten der posteriore laterale präfrontale Cortex und der orbitofrontale Cortex den motivationalen Kontext eines Trials anhand des Risikos des Verlustes von bisher investierter Anstrengung. Insgesamt weisen diese Befunde darauf hin, dass die rostrale cinguläre Zone eine entscheidende Rolle spielt für die Kontrolle sequenzieller Handlungsstufen, die auf eine verzögerte Belohnung ausgerichtet sind. Diese Kontrollfunktion scheint auf der kontinuierlichen Aktualisierung des Wertes einer Handlungsstufe zu basieren, der von der aktuellen Zielnähe bestimmt wird. Die Befunde der zweiten Studie lassen darauf schließen, dass sich die bisher investierte Anstrengung zur Erreichung eines Handlungsziels auf die Bereitstellung von allgemeinen kognitiven Ressourcen auswirkt. Das Risiko des Verlustes von bisher investierter Anstrengung kann außerdem ein kontextuelles Merkmal der Situation darstellen, das als Bezugsrahmen für die Evaluation des erwarteten Wertes dienen kann

Limits and dynamics of randomly connected neuronal networks

Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these random architectures on the dynamics of such networks, we analyze the mesoscopic and macroscopic limits of networks with random correlated connectivity weights and delays. We address both averaged and quenched limits, and show propagation of chaos and convergence to a complex integral McKean-Vlasov equations with distributed delays. We then instantiate a completely solvable model illustrating the role of such random architectures in the emerging macroscopic activity. We particularly focus on the role of connectivity levels in the emergence of periodic solutions

Synthesizing attractors of Hindmarsh-Rose neuronal systems

In this paper a periodic parameter switching scheme is applied to the Hindmarsh-Rose neuronal system to synthesize certain attractors. Results show numerically, via computer graphic simulations, that the obtained synthesized attractor belongs to the class of all admissible attractors for the Hindmarsh-Rose neuronal system and matches the averaged attractor obtained with the control parameter replaced with the averaged switched parameter values. This feature allows us to imagine that living beings are able to maintain vital behavior while the control parameter switches so that their dynamical behavior is suitable for the given environment.Comment: published in Nonlinear Dynamic